Find an explicit formula for the arithmetic sequence $-45,-30,-15,0,...$. Note: the first term should be $\textit{c(1)}$. $c(n)=$
The general explicit formula for arithmetic sequences is ${a_1}+{d}(n-1)$, where ${a_1}$ is the first term and $ d$ is the common difference. The first term is ${-45}$ and the common difference is ${15}$. ${+15\,\curvearrowright}$ ${+15\,\curvearrowright}$ ${+15\,\curvearrowright}$ ${-45},$ $-30,$ $-15,$ $0,...$ This is the explicit formula for the arithmetic sequence $-45,-30,-15,0,...$. $c(n)={-45}+{15}(n-1)$ Note that this solution strategy results in this formula, however an equally correct solution can be written in other equivalent forms as well.